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Assembly of actin subunits into actin filaments. An unseeded bulk reaction can show a actin nucleation lag, a growth phase and an approximately constant final polymer mass; equal endpoints need not imply equal kinetics.

A nonadsorbed chain section whose two ends connect to surface-bound portions of the same adsorbed polymer. Loops extend into the solvent and contribute to the thickness, steric repulsion and conformational entropy of an adsorbed layer.

Agarose gel electrophoresis uses a porous agarose polymer network. For linear double-stranded DNA within a suitable separation range, shorter fragments generally move farther in a fixed run. Raising the agarose concentration changes the mesh and the range of sizes that can be resolved.^[ref] A compact circular DNA molecule need not migrate like linear DNA of the same length: geometry affects passage through the mesh.^[ref]

A concrete laboratory example is Addgene's documented DNA separation protocol. Its standard 1% gel contains 1 g of agarose in 100 mL of TAE buffer. Dissolved agarose sets in a casting tray around a comb; removing the comb leaves sample wells. The gel is covered with the same buffer solution in a box connected to a voltage source. Loading buffer contains glycerol to increase sample density and a tracking dye to show run progress. A DNA ladder occupies a separate lane beside the samples. With wells near the negative cathode, DNA migrates toward the positive anode. After separation, bound stain makes the DNA visible by fluorescence under a UV transilluminator. The DNA ladder supplies the size reference; the tracking dye monitors migration but does not identify sample DNA.^[ref]

In the manufacturer's controlled comparison, the same DNA ladder runs in 1%, 2%, and 3% agarose gels with the same run time and other stated conditions. The changed gel band spacing shows why a calibration belongs to its particular gel conditions, rather than establishing a universal distance law.^[ref]

In interpreting an unknown sample, a blank lane tests for detectable background or carryover in that blank, while the DNA ladder checks migration and detection of its known fragments. An empty sample lane cannot by itself distinguish absent DNA from unsuccessful loading or insufficient detection. These controls answer different questions; neither makes matching migration a proof of matching nucleotide sequence.

A scaling model of overlapping end-grafted polymers assigns each chain a column of lateral width $D\sim s^{-1/2}$ at grafting density $s$. Each concentration blob contains $g\sim (D/a{)}^{1/\nu }$ statistical segments, and stacking $N/g$ blobs gives polymer brush height $H\sim ND/g$. For assumed segment volume $a^3$, the mean volume fraction is $\varphi \sim N{a}^{3}s/H$. It assumes a long many-segment-blob brush and supplies scaling powers rather than a precise chain-end distribution.

The Asakura-Oosawa model treats dilute nonadsorbing polymer coils as mutually interpenetrable ideal particles excluded from a layer around each colloid. For colloid radius $a$ and polymer exclusion thickness $R_g$, two exclusion spheres of radius $R_e=a+R_g$ overlap when $2a\le R<2R_e$. Adding their two spherical cap volumes gives $V_{\mathrm{ov}}=\pi (4R_e+R)(2R_e-R{)}^2/12$. Multiplication by $-{\Pi }_p$ gives the displayed pair free energy, with zero depletion interaction beyond $2R_e$. The range is controlled by polymer size and the depth by reservoir polymer concentration. At larger polymer concentration, polymer interactions and many-body overlap effects require care.

Beta-hydride elimination transfers hydrogen from the beta carbon of a metal-bound alkyl to the metal while forming an alkene. It can release a growing polymer chain and compete with migratory insertion. Its accessibility depends on geometry, available sites and bond energetics.

An incompressible, equal-site-volume mean-field approximation for two polymers of degrees of polymerization $N_A,N_B$. Here $f$ is mixing free energy per site and $\varphi$ is the volume fraction of species $A$. For a composition-independent Flory interaction parameter, local stability requires $1/(N_A\varphi )+1/[N_B(1-\varphi )]-2\chi >0$. The thermodynamic critical point is ${\varphi }_c=\sqrt{N_B}/(\sqrt{N_A}+\sqrt{N_B})$ and ${\chi }_c=(N_A^{-1/2}+N_B^{-1/2}{)}^2/2$.

A biopolymer is a polymer produced by a living system, including proteins, nucleic acids and polysaccharides. Local chemical structure, sequence and interactions can give it stiffness or preferred conformations beyond those of an ideal chain. Biopolymer mechanics uses models such as the worm-like chain and the helix-coil transition model to represent those features.

A polymer composed of connected blocks with different repeat-unit chemistry. Incompatible blocks can form spatially distinct domains while remaining covalently connected.

Chain-growth initiation creates a chain capable of chain-growth propagation. WriteThis schematic includes the first incorporated monomeric unit; any preceding production of $I^{\ast }$ is a separate step. If $C$ counts polymer molecules, $A$ counts polymer-bound polymerization-active sites, and $S$ counts incorporated monomeric units, this event changes $(C,A,S)$ by $(1,1,1)$. The free $I^{\ast }$ was excluded from $A$, so this does not assert creation of reactivity from nothing. An initiator feed amount need not equal the number of successful chains: the efficiency of forming productive chains and the number of initiating species per initiator matter. ^[ref]

In chain-growth polymerization, each growth step joins a monomer to a reactive site on a polymer chain and regenerates that reactive site. This is the precise mechanistic restriction in IUPAC's definition: growth occurs exclusively through these monomer–chain-site reactions. The word chain refers to the succession of site-regenerating chemical reactions. It does not merely mean that the product looks like a long chain. Chain-growth initiation starts this succession; chain-growth propagation continues it; chain-growth termination and chain transfer in chain polymerization can change its fate.^[ref]

The contrast with step-growth polymerization concerns the permitted joining partners. There, suitable reactive groups can join two existing chains, for example a two-unit chain and a three-unit chain. In chain-growth propagation, a free monomer adds to a polymerization-active site. Release of a small byproduct is a separate classification question: IUPAC explicitly allows condensative chain polymerization.^[ref] The useful consequence is that a few growing chains can incorporate many monomer molecules while much of the feed remains unreacted. Their degree of polymerization depends on how those units are shared among chains, as finite chain-growth bookkeeping makes explicit.

Chain-growth termination removes the ability of a reactive chain carrier to continue the succession of growth steps.^[ref] Two illustrative outcomes have different molecule counts:The first joins the two chains into one inactive polymer molecule. The second leaves two inactive polymer molecules, as can occur when one chain end transfers hydrogen to the other instead of their ends joining. End-group chemistry is suppressed in these unit-count symbols; they are not complete molecular formulas. Losing two polymerization-active sites does not mean losing two chains or any incorporated monomeric units. A temporarily inactive, reactivatable site must not be counted as irreversible chain-growth termination.

In chain transfer in chain polymerization, a growing chain can lose its polymerization-active site while another molecule acquires reactivity. In a common atom-transfer picture, the old chain becomes inactive and the new carrier can initiate further chain-growth propagation.^[ref] The number of reactive carriers can survive even though the identity of the growing chain changes. If the new carrier successfully starts a new chain, $C$ increases; a fixed active-carrier count therefore does not imply a fixed polymer molecule count. Whether transfer is irreversible, reversible, or involves an already existing chain matters for the final bookkeeping.

The change of an isolated flexible polymer from an expanded coil toward a dense polymer globule as its solvent becomes less favorable. In the Flory approximation, $F/(k_{B}T)\sim R^2/(N{a}^2)+v{N}^2/R^3+u{N}^3/R^6$, where the positive three-segment coefficient $u$ prevents collapse to zero size. Positive $v$ gives swollen-coil scaling, $v=0$ gives the theta temperature condition, and negative $v$ favors a dense state with $R^3\sim uN/|v|$. Finite chain length rounds the change; polymer aggregation is a distinct multi-chain process and must be controlled in an experiment.

A coil-stretch transition is a sharp change from a coiled to a substantially extended polymer conformation under sufficiently strong extensional flow. The driving extensional strain rate must compete with the chain's relaxation rate, and the available residence time matters. A long polymer relaxation time lets a weak but sustained flow produce a large effect. The Hookean dumbbell in planar extension below isolates this competition; its unbounded growth signals a model limitation, rather than a prediction of infinitely long molecules.

A polymer with an extended sequence of conjugated bonds along its backbone.

A polymer containing monomeric units derived from more than one monomer species.

The Cossee-Arlman mechanism propagates a polymer through alkene coordination followed by insertion into a metal–carbon bond. Repetition extends the metal-bound chain. Regioselectivity controls monomer connectivity; it does not by itself specify tacticity.

A cross-link connects different segments of a polymer network and restricts their independent motion. Permanent chemical cross-links commonly use covalent bonds; physical associations can instead have finite lifetimes. A connected permanent network can sustain long-time shear stress, whereas an uncrosslinked melt eventually flows. Cross-link density and network structure influence elastomer stiffness.

For a long self-avoiding polymer in a tube of diameter $D$, represent each confinement blob by $g$ statistical segments of length $b$, with $D\sim b{g}^{3/5}$. Excluded-volume repulsion orders the blobs along the tube, giving $X\sim (N/g)D=L(b/D{)}^{2/3}$. More generally, a segment excluded-volume parameter $v$ gives $X\sim L[v/(b{D}^2){]}^{1/3}$. This requires many blobs and $D$ smaller than the free coil size; $b\ll D\ll L$ alone does not ensure that. An ideal chain without intersegment repulsion is not a one-dimensional string of nonoverlapping blobs.